The online check-out works for me, so long as you check-in online too, and ideally do the Digital Key too. This is because (from what I can make out) the paperwork regarding payment is in the right place for check-out to operate tidily.

As mentioned up thread, you can't do this after the official check-out time, the app then greys out the option.

For the invoice delivery, I too have had mixed experience, and the website invoice copy works best in the USA and worse in the UK. But the app also has an invoice copy feature, which generally does work after a few days.